Preheat the oven to 350°F / 175°C. Butter and line an 8×4" loaf pan with parchment paper.
Add the butter and sugar to the bowl of a stand mixer fitted with a paddle attachment (Alternatively, you can use a hand mixer and a large mixing bowl.) Beat the butter and sugar on medium speed for 4 minutes.
With the mixer still running, beat in the eggs one at a time, beating for 30 seconds before adding in the next egg.
Beat in the sour cream and vanilla until well combined.
Add in the flour, baking powder, and salt. Mix on low speed just until the flour is completely incorporated.
Cinnamon Swirl
Remove about 1 ½ c. of batter and pour it into a small bowl. Carefully mix in the cinnamon and brown sugar until just combined.
Layer the pound cake into the prepared loaf pan. Pour ⅓ of the vanilla pound cake batter into the pan, then top it with ½ of the cinnamon batter.
Add in half of the remaining vanilla batter, followed by the rest of the cinnamon batter then the rest of the vanilla batter. Use a knife to gently swirl the batters together in the pan.
Bake the cake for 50-60 minutes, or until a toothpick inserted in the center of the cake comes out clean or with only a few moist crumbs.
Cream Cheese Icing
In a small mixing bowl, beat together the cream cheese and salt until well combined.
Add in the milk and vanilla and beat until no clumps remain, then beat in the powdered sugar until the icing is smooth.
Once the cake has come to room temperature, pour the icing over it. Slice, serve, and enjoy!